1. undefined term definition defined term space point line plane
collinear
coplanar
intersection
Vocabulary

2. Concept

3. A. Use the figure to name a line containing point K.
Name Lines and Planes
A. Use the figure to name a line containing point K.
Answer: The line can be named as line a.
There are three points on the line. Any two of the points can be used to name the line.
Example 1

4. B. Use the figure to name a plane containing point L.
Name Lines and Planes
B. Use the figure to name a plane containing point L.
You can also use the letters of any three noncollinear points to name the plane. plane JKM plane KLM plane JLM
Answer: The plane can be named as plane B.
Example 1

5. A. Use the figure to name a line containing the point X.
A. line X
B. line c
C. line Z D.
Example 1a

6. B. Use the figure to name a plane containing point Z.
A. plane XY
B. plane c
C. plane XQY
D. plane P
Example 1b

7. B. Use the figure to name a plane containing point Z.
A. plane XY
B. plane c
C. plane XQY
D. plane P
Example 1b

8. Draw a line anywhere on the plane.
Draw Geometric Figures
Draw a line anywhere on the plane.
Example 3

9. A. Choose the best diagram for the given relationship
A. Choose the best diagram for the given relationship. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Also, point F is on plane D and is not collinear with any of the three given lines.
A. B C. D.
Example 3a

10. A. How many planes appear in this figure?
Interpret Drawings
A. How many planes appear in this figure?
Answer: There are two planes: plane S and plane ABC.
Example 4

11. A. How many planes appear in this figure?
A. one
B. two
C. three
D. four
Example 4a

12. End of the Lesson

13. What is another name for AB?
A. AA
B. AT
C. BQ
D. QB
5-Minute Check 2

14. Name the intersection of planes Z and W.
A. BZ
B. AW
C. AB
D. BQ
5-Minute Check 4

15. Name the intersection of planes Z and W.
A. BZ
B. AW
C. AB
D. BQ
5-Minute Check 4

16. Which of the following statements is always false?
A. The intersection of a line and a plane is a point.
B. There is only one plane perpendicular to a given plane.
C. Collinear points are also coplanar.
D. A plane contains an infinite number of points.
5-Minute Check 6

17. line segment betweenness of points between congruent segments
construction
Vocabulary

18. Concept

19. Find BD. Assume that the figure is not drawn to scale.
16.8 mm
50.4 mm
Find BD. Assume that the figure is not drawn to scale.
A mm
B mm
C mm
D. 84 mm
Example 3

20. Find LM. Assume that the figure is not drawn to scale.
Find Measurements by Subtracting
Find LM. Assume that the figure is not drawn to scale.
Point M is between L and N.
LM + MN = LN Betweenness of points
LM = 4 Substitution
LM – 2.6 = 4 – 2.6 Subtract 2.6 from each side.
LM = 1.4 Simplify.
Example 4

21. Find TU. Assume that the figure is not drawn to scale.V
3 in A. B. C. D.
in.
Example 4

22. Draw a figure to represent this situation.
Write and Solve Equations to Find Measurements
ALGEBRA Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.
Draw a figure to represent this situation.
ST + TU = SU Betweenness of points
7x + 5x – 3 = 45 Substitute known values.
7x + 5x – = Add 3 to each side.
12x = 48 Simplify.
Example 5

23. x = 4 Simplify. Now find ST. ST = 7x Given = 7(4) x = 4 = 28 Multiply.
Write and Solve Equations to Find Measurements
x = 4 Simplify.
Now find ST.
ST = 7x Given
= 7(4) x = 4
= 28 Multiply.
Answer: x = 4, ST = 28
Example 5

24. x = 4 Simplify. Now find ST. ST = 7x Given = 7(4) x = 4 = 28 Multiply.
Write and Solve Equations to Find Measurements
x = 4 Simplify.
Now find ST.
ST = 7x Given
= 7(4) x = 4
= 28 Multiply.
Answer: x = 4, ST = 28
Example 5

25. Splash Screen

26. What is the value of x and AB if B is between A and C, AB = 3x + 2, BC = 7, and AC = 8x – 1?
A. x = 2, AB = 8
B. x = 1, AB = 5 C.
D. x = –2, AB = –4
5-Minute Check 1

27. If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1, what is the value of x and MN?
A. x = 1, MN = 0
B. x = 2, MN = 1
C. x = 3, MN = 2
D. x = 4, MN = 3
5-Minute Check 2

28. distance
irrational number
midpoint
segment bisector
Vocabulary

29. Concept

30. Use the number line to find QR.
Find Distance on a Number Line
Use the number line to find QR.
The coordinates of Q and R are –6 and –3.
QR = | –6 – (–3) | Distance Formula
= | –3 | or 3 Simplify.
Answer: 3
Example 1

31. Use the number line to find AX.
C. –2
D. –8
Example 1

32. Concept

33. Find the distance between E(–4, 1) and F(3, –1).
Find Distance on a Coordinate Plane
Find the distance between E(–4, 1) and F(3, –1).
(x1, y1) = (–4, 1) and (x2, y2) = (3, –1)
Example 2

34. Concept

35. Find Midpoint in Coordinate Plane
Answer: (–3, 3)
Example 4

36. Use Algebra to Find Measures
Understand You know that Q is the midpoint of PR, and the figure gives algebraic measures for QR and PR. You are asked to find the measure of PR.
Example 6

37. Plan Because Q is the midpoint, you know that
Use Algebra to Find Measures
Plan Because Q is the midpoint, you know
that
Use this equation and the algebraic measures to find a value for x.
Solve
Subtract 1 from each side.
Example 6

38. Use Algebra to Find Measures
Original measure
Example 6

39. QR = 6 – 3x Original Measure
Use Algebra to Find Measures
Check
QR = 6 – 3x Original Measure
Example 6

40. Use Algebra to Find Measures
Multiply.
Simplify.
Example 6

41. Splash Screen

42. Use the number line to find the measure of DE.
C. 7
D. 9
5-Minute Check 2

43. Find the distance between P(–2, 5) and Q(4, –3).
5-Minute Check 4

44. Find the coordinates of R if M(–4, 5) is the midpoint of RS and S has coordinates (0, –10).
B. (–4, 15)
C. (–2, –5)
D. (2, 20)
5-Minute Check 5

45. ray degree right angle acute angle opposite rays angle obtuse angle
angle bisector
opposite rays
angle
side
vertex
interior
exterior
Vocabulary

46. A. Name all angles that have B as a vertex.
Angles and Their Parts
A. Name all angles that have B as a vertex.
Answer:
Example 1

47. Angles and Their Parts
B. Name the sides of 5.
Answer:
Example 1

48. Angles and Their Parts C.
Example 1

49. B. A. B. C.
D. none of these
Example 1b

50. Concept

51. A. Measure TYV and classify it as right, acute, or obtuse.
Measure and Classify Angles
A. Measure TYV and classify it as right, acute, or obtuse.
Answer: mTYV = 90, so TYV is a right angle.
Example 2

52. A. Measure CZD and classify it as right, acute, or obtuse.
A. 30°, acute
B. 30°, obtuse
C. 150°, acute
D. 150°, obtuse
Example 2a

53. Measure and Classify Angles
INTERIOR DESIGN Wall stickers of standard shapes are often used to provide a stimulating environment for a young child’s room. A five-pointed star sticker is shown with vertices labeled. Find mGBH and mHCI if GBH  HCI, mGBH = 2x + 5, and mHCI = 3x – 10.
Example 3

54. mGBH = mHCI Definition of congruent angles
Measure and Classify Angles
Step 1 Solve for x.
GBH  HCI Given
mGBH = mHCI Definition of congruent angles
2x + 5 = 3x – 10 Substitution
2x + 15 = 3x Add 10 to each side.
15 = x Subtract 2x from each side.
Example 3

55. Step 2 Use the value of x to find the measure of either angle.
Measure and Classify Angles
Step 2 Use the value of x to find the measure of either angle. .
Answer: mGBH = 35, mHCI = 35
Example 3

56. Splash Screen

57. Refer to the figure. Name the vertex of 3.
A. A
B. B
C. C
D. D
5-Minute Check 1

58. Refer to the figure. Name a point in the interior of ACB.
A. G
B. D
C. B
D. A
5-Minute Check 2

59. Refer to the figure. Which ray is a side of BAC?
A. DB
B. AC
C. BD
D. BC
5-Minute Check 3

60. Refer to the figure. Name an angle with vertex B that appears to be acute.
A. ABG
B. ABC
C. ADB
D. BDC
5-Minute Check 4

61. Refer to the figure. If bisects ABC, mABD = 2x + 3, and mDBC = 3x – 13, find mABD.
5-Minute Check 5

62. OP bisects MON and mMOP = 40°. Find the measure of MON.
5-Minute Check 6

63. adjacent angles linear pair vertical angles complementary angles
supplementary angles
perpendicular
Vocabulary

64. Concept

65. Sample Answers: PIU and RIS, PIQ and TIS, QIR and TIU
Identify Angle Pairs
B. ROADWAYS Name an angle pair that satisfies the condition two acute vertical angles.
Sample Answers: PIU and RIS, PIQ and TIS, QIR and TIU
Example 1

66. B. Name two acute vertical angles.
A. BAN and EAD
B. BAD and BAN
C. BAC and CAE
D. FAN and DAC
Example 1b

67. A. Name two adjacent angles whose sum is less than 90.
A. CAD and DAE
B. FAE and FAN
C. CAB and NAB
D. BAD and DAC
Example 1a

68. Concept

69. Plan Draw two figures to represent the angles.
Angle Measure
ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle.
Understand The problem relates the measures of two supplementary angles. You know that the sum of the measures of supplementary angles is 180.
Plan Draw two figures to represent the angles.
Example 2

70. Solve 6x – 6 = 180 Simplify. 6x = 186 Add 6 to each side.
Angle Measure
Solve
6x – 6 = 180 Simplify.
6x = 186 Add 6 to each side.
x = 31 Divide each side by 6.
Example 2

71. Use the value of x to find each angle measure.
mA = x mB = 5x – 6
= = 5(31) – 6 or 149
Check Add the angle measures to verify that the angles are supplementary.
mA + mB = 180
= 180
180 = 180 
Answer: mA = 31, mB = 149
Example 2

72. ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other.
A. 1°, 1°
B. 21°, 111°
C. 16°, 74°
D. 14°, 76°
Example 2

73. Concept

74. ALGEBRA Find x and y so that KO and HM are perpendicular.
Perpendicular Lines
ALGEBRA Find x and y so that KO and HM are perpendicular.
Example 3

75. 84 = 12x Subtract 6 from each side. 7 = x Divide each side by 12.
Perpendicular Lines
90 = (3x + 6) + 9x Substitution
90 = 12x + 6 Combine like terms.
84 = 12x Subtract 6 from each side.
7 = x Divide each side by 12.
Example 3

76. 84 = 3y Subtract 6 from each side. 28 = y Divide each side by 3.
Perpendicular Lines
To find y, use mMJO.
mMJO = 3y + 6 Given
90 = 3y + 6 Substitution
84 = 3y Subtract 6 from each side.
28 = y Divide each side by 3.
Answer: x = 7 and y = 28
Example 3

77. A. x = 5
B. x = 10
C. x = 15
D. x = 20
Example 3

78. Concept

79. A. Determine whether the statement mXAY = 90 can be assumed from the figure.
A. yes
B. no
Example 4a

80. B. Determine whether the statement TAU is complementary to UAY can be assumed from the figure.
A. yes
B. no
Example 4b

81. C. Determine whether the statement UAX is adjacent to UXA can be assumed from the figure.
A. yes
B. no
Example 4c

82. Assignment:
Read Pg. 78
Pg. 78/ 1-31
Pg. 83/ 1-19